If `a_(1),a_(2),a_(3),......,a_(20)` are A.M's inserted between `13` and `67`, then the maximum value of product `a_(1)a_(2)a_(3)......a_(20)` is

If a_(1),a_(2),a_(3),...a_(n) are positive real numbers whose product is a fixed number c, then the minimum value of a_(1)+a_(2)+....+a_(n-1)+2a_(n) is

If a_(1),a_(2),a_(3),a_(4) are positive real numbers such that a_(1)+a_(2)+a_(3)+a_(4)=16 then find maximum value of (a_(1)+a_(2))(a_(3)+a_(4))

If n arithmetic means A_(1),A_(2),---,A_(n) are inserted between a and b then A_(2)=

If terms a_(1),a_(2),a_(3)...,a_(50) are in A.P and a_(6)=2, then the value of common difference at which maximum value of a_(1)a_(4)a_(5) occur is

If A_(1), A_(2), A_(3),....A_(51) are arithmetic means inserted between the number a and b, then find the value of ((b + A_(51))/(b - A_(51))) - ((A_(1) + a)/(A_(1) - a))

If A_(1),A_(2),A_(3),A_(2) and A_(5) are the five A.M.'s between 2 and 8 ,then find the value of A_(1)+A_(2)+A_(3)+A_(4)+A_(5)

If a_(1)+a_(2)+a_(3)+a_(4)+a_(5)...+a_(n) for all a_(i)>0,i=1,2,3dots n. Then the maximum value of a_(1)^(2)a_(2)a_(3)a_(4)a_(5)..a_(n) is

If a_(1)=2 and a_(n)-a_(n-1)=2n(n>=2), find the value of a_(1)+a_(2)+a_(3)+....+a_(20)

Let a_(1)=0 and a_(1),a_(2),a_(3),...,a_(n) be real numbers such that |a_(i)|=|a_(i-1)+1| for all i then the A.M.of the numbers a_(1),a_(2),a_(3),...,a_(n) has the value A where